Radon-222 is a radioactive gas with a half-life of 4 days. Approximately how much of a 40 g sample of radon-222 would remain after 12 days?
To determine the amount of radon-222 remaining after 12 days, we need to consider its half-life.
The half-life of a substance is the time it takes for half of the original sample to decay. In this case, radon-222 has a half-life of 4 days, which means that after each 4-day interval, half of the remaining radon-222 will decay.
To solve this problem, we can calculate the number of half-lives that pass within the given time period and use that to determine the remaining amount of radon-222.
Here's how to do it step by step:
Step 1: Calculate the number of half-lives within 12 days.
Since the half-life is 4 days, we divide the total time (12 days) by the half-life:
12 days / 4 days = 3 half-lives
Step 2: Calculate the remaining fraction of radon-222 after 3 half-lives.
Each half-life reduces the amount of radon-222 by half, so after 3 half-lives, the remaining fraction is (1/2)^3.
Step 3: Calculate the remaining amount of radon-222.
Multiply the fraction remaining by the original sample size:
Remaining amount = (1/2)^3 * 40 g
Now let's calculate it:
Remaining amount = (1/8) * 40 g
Remaining amount = 5 g
Therefore, approximately 5 grams of the 40 g sample of radon-222 would remain after 12 days.